"Solutions to the RH and and related mathematical research areas

 Disclaimer: with the exception of the last section D all papers of this page are without authorization from the ivory tower

                     for the latest updated version see  http://www.fuchs-braun.com

Braun K., Three Millennium problems, RH, NSE, YME, OVERVIEW, August 11, 2018.pdf [ 707.2 KB ]

A. A Kummer function based Zeta function theory

to prove the Riemann Hypothesis

The Riemann Zeta function

                                 http://www.riemann-hypothesis.de

Braun K., An alternative entire Zeta function representation and its related duality equation.pdf [ 235.7 KB ]

Braun K., A Kummer function based Zeta function theory to prove the Riemann Hypothesis and the Goldbach conjecture.pdf [ 3.3 MB ]

B. A new ground state energy model of the harmonic quantum oscillator

www.yang-mills-equations.de

www.quantum-gravity.de

The Bose-Einstein condensate

 Abstract

We provide a new ground state energy model which ensures convergent quantum oscillator energy series. This enables the definition of a truly infinitesimal geometry based on a non-ordered, still Archimedian field. The corresponding inner product with its induced norm defines the appropriate metric. The (Hilbert space) domains of related self-adjoint, positive definite operators to build appropriate eigenpair structures are built on Cartan´s differential forms. By this, H. Weyl´s "truly" infinitesimal (affine connexions, parallel displacements, differentiable manifolds based) geometry is replaced by a truly infinitesimal (rotation group based) geometry (corresponding to continuous manifolds, only):

Braun K., An alternative Schroedinger (Calderon) momentum operator enabling a quantum gravity model.pdf [ 1 MB ]

Braun K., Unusual Hilbert or Hoelder space frames for the elementary particles transport (Vlasov) equation.pdf [ 1.1 MB ]

May 2017 summary

Braun K., Comparison table, math. modelling frameworks for SMEP and GUT.pdf [ 896.8 KB ]

A new H(-1/2) Hilbert space based ground state energy model of the harmonic quantum oscillator

August 2013, A new ground state energy model.pdf [ 1.1 MB ]

 Relationships/opportunities to a related quantum gravity model

update Dec 6, 2013

A quantum gravity and ground state energy Hilbert space model.pdf [ 739.5 KB ]

Further related/supporting papers

                   Braun K., "An alternative quantization of H=xp"

       http://www.fuchs-braun.com/media/e9ed39ef818176fffff8031fffffff2.pdf

Braun K., Hilbert transformation, Gaussian and Dawson function, and the Harmonic Quantum Oscillator Model.pdf [ 379.5 KB ]

Nov 2011, Thoughts about a Quantum Gravity Theory.pdf [ 783.5 KB ]

June 2013, Quantum gravity model related mathematical areas.pdf [ 2.6 MB ]

Riesz operators and rotations.pdf [ 118.7 KB ]

Hardy Spaces, Hyperfunctions, Pseudo-Differential Operators and Wavelets.pdf [ 547.5 KB ]

C. A global unique weak H(-1/2) solution of the Navier-Stokes initial value problem 

Braun K., Global existence and uniqueness of 3D Navier-Stokes equations.pdf [ 753.8 KB ]

Braun K., Unusual Hilbert or Hoelder space frames for the elementary particles transport (Vlasov) equation.pdf [ 1 MB ]

earlier published versions

Braun K., Global existence and uniqueness of 3D Navier-Stokes equations, Jan 2016.pdf [ 474.8 KB ]

Braun K., Global existence and uniqueness of 3D Navier-Stokes equations, April 2016.pdf [ 584.2 KB ]

D. PhD thesis

June 1986, Interior error estimates of the Ritz method for Pseudo-Differential equations.pdf [ 2.4 MB ]

Besides the interior error estimates the paper proves the quasi-optimal approximation behavior of the Ritz-Galerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (Pseudo-Differential) integral operator. Other examples would be the Calderon-Zygmund (singular integral) operator or the Hilbert transform (singular integral) operator.